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SubjectUnbound(?) internal fragmentation in Btrfs
Hello everyone.

I was asked to review/evaluate Btrfs for using in enterprise
systems and the below are my first impressions (linux-2.6.33).

The first test I have made was filling an empty 659M (/dev/sdb2)
btrfs partition (mounted to /mnt) with 2K files:

# for i in $(seq 1000000); \
do dd if=/dev/zero of=/mnt/file_$i bs=2048 count=1; done
(terminated after getting "No space left on device" reports).
# ls /mnt | wc -l
59480
So, I got the "dirty" utilization 59480*2048 / (659*1024*1024) = 0.17,
and the first obvious question is "hey, where are other 83% of my
disk space???" I looked at the btrfs storage tree (fs_tree) and was
shocked with the situation on the leaf level. The Appendix B shows
5 adjacent btrfs leafs, which have the same parent.

For example, look at the leaf 29425664: "items 1 free space 3892"
(of 4096!!). Note, that this "free" space (3892) is _dead_: any
attempts to write to the file system will result in "No space left
on device".

Internal fragmentation (see Appendix A) of those 5 leafs is
(1572+3892+1901+3666+1675)/4096*5 = 0.62. This is even worse then
ext4 and xfs: The last ones in this example will show fragmentation
near zero with blocksize <= 2K. Even with 4K blocksize they will
show better utilization 0.50 (against 0.38 in btrfs)!

I have a small question for btrfs developers: Why do you folks put
"inline extents", xattr, etc items of variable size to the B-tree
in spite of the fact that B-tree is a data structure NOT for variable
sized records? This disadvantage of B-trees was widely discussed.
For example, maestro D. Knuth warned about this issue long time
ago (see Appendix C).

It is a well known fact that internal fragmentation of classic Bayer's
B-trees is restricted by the value 0.50 (see Appendix C). However it
takes place only if your tree contains records of the _same_ length
(for example, extent pointers). Once you put to your B-tree records
of variable length (restricted only by leaf size, like btrfs "inline
extents"), your tree LOSES this boundary. Moreover, even worse:
it is clear, that in this case utilization of B-tree scales as zero(!).
That said, for every small E and for every amount of data N we
can construct a consistent B-tree, which contains data N and has
utilization worse then E. I.e. from the standpoint of utilization
such trees can be completely degenerated.

That said, the very important property of B-trees, which guarantees
non-zero utilization, has been lost, and I don't see in Btrfs code any
substitution for this property. In other words, where is a formal
guarantee that all disk space of our users won't be eaten by internal
fragmentation? I consider such guarantee as a *necessary* condition
for putting a file system to production.

Any technical comments are welcome.

Thanks,
Edward.


Appendix A.
-----------
Glossary
1. Utilization of data and(or) metadata storage.

The fraction A/B, where
A is total size in bytes of stored data and(or) metadata.
B = N * S, where
N is number of blocks occupied by stored data and(or) metadata.
S is block size in bytes.

2. Internal fragmentation of data and(or) metadata storage.

difference (1 - U), where U is utilization.

Appendix B.
-----------
a "period" in the dump of the fs_tree (btrfs-debug-tree /dev/sdb2)
...

leaf 29982720 items 4 free space 1572 generation 8 owner 5
fs uuid 50268d9d-2a53-4f4d-b3a3-4fbff74dd956
chunk uuid 963ba49a-bb2b-48a3-9b35-520d857aade6
item 0 key (319 XATTR_ITEM 3817753667) itemoff 3917 itemsize 78
location key (0 UNKNOWN 0) type 8
namelen 16 datalen 32 name: security.selinux
item 1 key (319 EXTENT_DATA 0) itemoff 1848 itemsize 2069
inline extent data size 2048 ram 2048 compress 0
item 2 key (320 INODE_ITEM 0) itemoff 1688 itemsize 160
inode generation 8 size 2048 block group 29360128 mode
100644 links 1
item 3 key (320 INODE_REF 256) itemoff 1672 itemsize 16
inode ref index 65 namelen 6 name: file64
leaf 29425664 items 1 free space 3892 generation 8 owner 5
fs uuid 50268d9d-2a53-4f4d-b3a3-4fbff74dd956
chunk uuid 963ba49a-bb2b-48a3-9b35-520d857aade6
item 0 key (320 XATTR_ITEM 3817753667) itemoff 3917 itemsize 78
location key (0 UNKNOWN 0) type 8
namelen 16 datalen 32 name: security.selinux
leaf 29990912 items 1 free space 1901 generation 8 owner 5
fs uuid 50268d9d-2a53-4f4d-b3a3-4fbff74dd956
chunk uuid 963ba49a-bb2b-48a3-9b35-520d857aade6
item 0 key (320 EXTENT_DATA 0) itemoff 1926 itemsize 2069
inline extent data size 2048 ram 2048 compress 0
leaf 29986816 items 3 free space 3666 generation 8 owner 5
fs uuid 50268d9d-2a53-4f4d-b3a3-4fbff74dd956
chunk uuid 963ba49a-bb2b-48a3-9b35-520d857aade6
item 0 key (321 INODE_ITEM 0) itemoff 3835 itemsize 160
inode generation 8 size 2048 block group 29360128 mode
100644 links 1
item 1 key (321 INODE_REF 256) itemoff 3819 itemsize 16
inode ref index 66 namelen 6 name: file65
item 2 key (321 XATTR_ITEM 3817753667) itemoff 3741 itemsize 78
location key (0 UNKNOWN 0) type 8
namelen 16 datalen 32 name: security.selinux
leaf 29995008 items 3 free space 1675 generation 8 owner 5
fs uuid 50268d9d-2a53-4f4d-b3a3-4fbff74dd956
chunk uuid 963ba49a-bb2b-48a3-9b35-520d857aade6
item 0 key (321 EXTENT_DATA 0) itemoff 1926 itemsize 2069
inline extent data size 2048 ram 2048 compress 0
item 1 key (322 INODE_ITEM 0) itemoff 1766 itemsize 160
inode generation 8 size 2048 block group 29360128 mode
100644 links 1
item 2 key (322 INODE_REF 256) itemoff 1750 itemsize 16
inode ref index 67 namelen 6 name: file66
...

Appendix C.
-----------
D.E. Knuth, The Art of Computer Programming, vol. 3 (Sorting and Searching),
Addison-Wesley, Reading, MA, 1973.

--
Edward O. Shishkin
Principal Software Engineer
Red Hat Czech



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